Optimizing image recognition results for unknown labels
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A likely explanation is that the animals in the "nothing" group do not have much in common with each other.

This means it will be difficult for the network to learn which features from the images are associated with that label (in fact, there aren't any!). As a result, the network is probably assigning very low confidence to any estimate for the nothing label. You should be able to check if this is the case (i.e. examine whether it is ever confident about the label "nothing").

I am not completely sure how the Inception network encodes its labels. A common scheme though is to use one output neuron for each class. The correct label for an image is thus always a "1-hot" vector, where one of the elements is set to 1, and the others all to zero.

If that representation is being used, you can incorporate the "nothing" data by labelling it with a vector that is all zero: none of the output neurons should activate for it. That would produce precisely the training signal you want.